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Our goal is to build triangulations of the eight-dimensional torus with 511 vertices, 511 being the smallest number of vertices of the known triangulations of the torus. We define the separating maps from the lattice E 8   to Z / 511 Z and we establish the list of such maps up to symmetry.

Separating Maps of the Lattice E 8 and Triangulations of the Eight-Dimensional Torus